This research is intended to comprehend the vibration response of two types of flat plates, rectangular and circular, when all their boundaries are constrained and they are in free vibration. These structures are common in aerospace components, mechanical enclosures, and civil structures where vibration parameters like natural frequency and mode shape decide their performance and reliability. We used three methods to research this: classical analytical models in terms of plate theory and Bessel functions, numerical analysis in ANSYS APDL, and Python customized code to model the theoretical calculations and show the vibrational response. The Python code computed the first 10 natural frequencies and plotted mode shape plots, which correlated well with analytical values at low modes and were useful in assessing where analytical models start deviating. For rectangular plates, analytical and simulation convergence was strong for the first mode with less than 1% deviation, but the deviation increased for higher-order modes, reaching 29%. For circular plates, analytical values were good for simple symmetric modes, but they were large for higher-order modes, particularly with non-symmetric or degenerate patterns, where the deviation was more than 180%. These deviations showed the limitation of classical theory with complex vibration nature. The ANSYS simulations with high-resolution meshing and accurate boundary conditions were the benchmark to verify these deviations. The Python implementation not only confirmed the analytical results but provided an open and convenient platform for mode shape visualization, useful both in academic and engineering fields. Overall, this study confirms the benefit of combining analytical methods with computational and simulation approaches in a bid to better understand plate vibrations. It also provides an easy, open-source platform for further vibration analysis of structural components research that can be applied on a wide range of industries like aerospace, civil, and mechanical engineering.
Keywords:
Natural frequency, mode shapes, plate vibration, ANSYS simulation, Python modeling